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Graduate Theses and Dissertations Graduate School

2010

Modeling the locked-wheel skid tester to determinethe effect of pavement roughness on theInternational Friction IndexPatrick CummingsUniversity of South Florida

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Scholar Commons CitationCummings, Patrick, "Modeling the locked-wheel skid tester to determine the effect of pavement roughness on the InternationalFriction Index" (2010). Graduate Theses and Dissertations.http://scholarcommons.usf.edu/etd/1604

 

 

Modeling the Locked-Wheel Skid Tester to Determine the Effect of Pavement Roughness

on the International Friction Index

by

Patrick Cummings

A thesis submitted in partial fulfillment of the requirements for the degree of

Master of Science in Civil Engineering Department of Civil and Environmental Engineering

College of Engineering University of South Florida

Major Professor: Manjriker Gunaratne, Ph.D. Abdul Pinjari, Ph.D.

Qing Lu, Ph.D.                    

Date of Approval: June 11, 2010

Keywords: speed constant, dynamic load coefficient, measured skid number, friction prediction, megatexure

Copyright © 2010 , Patrick Cummings

 

 

DEDICATION

I dedicate this manuscript to my wife Heather, without whom I would not have

had the courage to finish, and to my parents Russell and Marcie, who instilled in me the

thirst for knowledge.

 

 

ACKNOWLEDGMENTS

I would like to thank Dr. Manjriker Gunaratne for giving me the opportunity to

participate in the Masters Degree program. He inspired and provoked the thoughts related

to this manuscript. I would also like to thank Dr. Abdul Pinjari and Dr. Qing Lu for

agreeing to serve on my committee. Special thanks to the members of my research group

who helped me to complete my research and testing.

 

i

 

TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES iv ABSTRACT vi CHAPTER 1 INTRODUCTION 1

1.1 Background 1 1.2 Principles of Pavement Friction 2 1.3 Locked-Wheel Skid Tester 4 1.4 Limitations of the International Friction Index 5 1.5 Objectives of Study 6

CHAPTER 2 EXPERIMENTAL ANALYSIS AND RESULTS 7 2.1 Proposed Vibration Modeling System 7 2.2 Verification of the Program 9 2.2.1 Modeling of a Two Degree of Freedom System Without Damping 9 2.2.2 Modeling of an Uncoupled Two Degree of Freedom System

With Damping 10 2.2.3 Modeling of a One Degree of Freedom System With Damping 12 2.3 Determination of LWT Parameters Using Modeling Techniques 15 2.4 Verification of LWT Parameters Using Field Measurements 16 2.5 Determination of the Relationship Between the Friction and Normal

Loads 19 2.6 Verification of Friction Load Modeling 25 2.7 Modeling the Effects of Pavement Roughness on the IFI 27 2.8 Field Verification of the Effects of Pavement Roughness on the IFI 32 2.9 Modeling the Effects of the Normal Load versus Friction Load

Relationship 34 2.10 Alternative Method for Determining Relationship Between SN and Normal Load 37 CHAPTER 3 CONCLUSIONS AND RECOMMENDATIONS 40

3.1 Current Research Proponents 40 3.2 Contribution 1 – Theoretical Prediction of LWT Friction Values 40

 

ii

 

3.3 Contribution 2 - Effects of Pavement Roughness on the IFI 41 3.4 Contribution 3 - Effects of Frictional Dependency on Normal Load on the IFI 41

LIST OF REFERENCES 42

 

iii

 

LIST OF TABLES

Table 2-1: Model Parameters for a Two Degree of Freedom System Without Damping 10

Table 2-2: Model Parameters for a Two Degree of Freedom System With Damping 11

Table 2-3: Model Parameters for a One Degree of Freedom System Restricting the Motion of M2 13

Table 2-4: Model Parameters for a One Degree of Freedom System Restricting the Motion of M1 14

Table 2-5: Parameters of a Two Degree of Freedom System Representing the LWT 16

Table 2-6: Parameters for the SN vs. W Relationship for Pavements C and D

(Fuentes et al., 2010) 20

Table 2-7: Parameters for Projection of SN vs. Normal Load Relationship Across a Range of Speeds for Pavement C (Fuentes et al., 2010) 24

Table 2-8: Parameters for Projection of SN vs. Normal Load Relationship Across a Range of Speeds for Pavement D (Fuentes et al., 2010) 24

Table 2-9: Inputs for Frequency Variation Analysis (A = 0.25 m) 28 Table 2-10: Results of Frequency Variation Analysis on Pavements C and D 29 Table 2-11: Inputs for Frequency Variation Analysis (ω = 0.05 Hz) 30 Table 2-12: Results of Amplitude Variation Analysis on Pavements C and D 31 Table 2-13: Results from Pavement Roughness Analysis on Pavement B 33 Table 2-14: Results from Pavement Roughness Analysis on Pavement I 34 Table 2-15: Results from ΔSN Variation Analysis on Pavements C, E, F, and G 37 

 

iv

 

LIST OF FIGURES

Figure 2-1: Two Degree of Freedom System with Displacement Input 7 Figure 2-2: Frequency Spectrum of a Two Degree of Freedom System Without

Damping 11

Figure 2-3: Frequency Spectrum of a Two Degree of Freedom System With Damping 12

Figure 2-4: Frequency Spectrum of the One Degree of Freedom System Restricting the Motion of M2 14

Figure 2-5: Frequency Spectrum of the One Degree of Freedom System Restricting the Motion of M1 15

Figure 2-6: Frequency Spectrum of a Two Degree of Freedom System Representing the LWT 16

Figure 2-7: Longitudinal Profile of Pavement H 17 Figure 2-8: Comparison of Experimental and Modeled Response of LWT at

20 mph 18 Figure 2-9: Comparison of Experimental and Modeled Response of LWT at

40 mph 18

Figure 2-10: Comparison of Experimental and Modeled Response of LWT at 60 mph 19

Figure 2-11: SN vs. W Relationship at 30 mph (Fuentes et al., 2010) 21 Figure 2-12: SN vs. W Relationship at 55 mph (Fuentes et al., 2010) 21 Figure 2-13: Derived Relationship of Frictional Force to Normal Load at 30 mph 22 Figure 2-14: Derived Relationship of Frictional Force to Normal Load at 55 mph 22 Figure 2-15: Relationship between SNi and Speed 23

 

v

 

Figure 2-16: Relationship between SNr and Speed 23 Figure 2-17: Relationship of SN vs. Normal Load for Pavement H at 55 mph 26 Figure 2-18: Relationship of Friction Load vs. Normal Load for Pavement H

at 55 mph 26

Figure 2-19: Comparison of Model Prediction to the Results of Friction Tests 27 Figure 2-20: Frequency Variation Effects on the Friction-Speed Relationship of

Pavement C 28

Figure 2-21: Frequency Variation Effects on the Friction-Speed Relationship of Pavement D 29

Figure 2-22: Amplitude Variation Effects on the Friction-Speed Relationship of Pavement C 30

Figure 2-23: Amplitude Variation Effects on the Friction-Speed Relationship of Pavement D 31

Figure 2-24: Effect of Pavement Roughness on IFI Parameters for Pavement B 33 Figure 2-25: Effect of Pavement Roughness on IFI Parameters for Pavement I 33 Figure 2-26: Skid Relationship of SN vs. Normal Load for Pavements C, E, F,

and G at 55 mph 35

Figure 2-27: Variation in ΔSN versus Speed for Pavements C, E, F, and G 36 Figure 2-28: Effects of Variation in ΔSN for Pavements C, E, F, and G with

Speed 36

Figure 2-29: Relationship of SN vs. Normal Load for Pavement A at 25, 40, and 55 mph Using Schallamach’s Equation 38 Figure 2-30: Relationship of SN vs. Normal Load for Pavement I at 20, 30, and 40 mph Using Schallamach’s Equation 39

 

vi

 

Modeling the Locked-Wheel Skid Tester to Determine the Effect of Pavement

Roughness on the International Friction Index

Patrick Cummings

ABSTRACT

Pavement roughness has been found to have an effect on the coefficient of friction

measured with the Locked-Wheel Skid Tester (LWT) with measured friction decreasing

as the long wave roughness of the pavement increases. However, the current pavement

friction standardization model adopted by the American Society for Testing and

Materials (ASTM), to compute the International Friction Index (IFI), does not account for

this effect. In other words, it had been previously assumed that the IFI’s speed constant

(SP), which defines the gradient of the pavement friction versus speed relationship, is an

invariant for any pavement with a given mean profile depth (MPD), regardless of its

roughness. This study was conducted to quantify the effect of pavement roughness on the

IFI’s speed constant. The first phase of this study consisted of theoretical modeling of the

LWT using a two-degree of freedom vibration system. The model parameters were

calibrated to match the measured natural frequencies of the LWT. The calibrated model

was able to predict the normal load variation during actual LWT tests to a reasonable

accuracy. Furthermore, by assuming a previously developed skid number (SN) versus

normal load relationship, even the friction profile of the LWT during an actual test was

predicted reasonably accurately. Because the skid number (SN) versus normal load

 

vii

 

relationship had been developed previously using rigorous protocol, a new method that is

more practical and convenient was prescribed in this work. This study concluded that

higher pavement long-wave roughness decreases the value of the SP compared to a

pavement with identical MPD but lower roughness. Finally, the magnitude of the loss of

friction was found to be governed by the non-linear skid number versus normal load

characteristics of a pavement.

 

1

 

CHAPTER 1

INTRODUCTION

1.1 Background

Evaluation and maintenance of friction in all pavement sections of a highway

network is a crucial task of transportation safety programs. The frictional interaction

between vehicle tires and pavement has been studied at many levels, and significant

efforts have been made to determine the factors that govern its mechanism. In early

stages of highway pavement maintenance, pavement friction was measured and

quantified using static testing devices combined with theoretical physical models. At that

time, the principal attributes of friction were assumed to be centered solely on pavement

texture. As technology improved, full-scale dynamic friction testing devices that

resembled the vehicles in motion in terms of the magnitude of pavement friction

experienced, were developed.

It has been found recently that pavement friction is, in fact, governed by several

factors including pavement lubrication, pavement roughness, and vehicle behavior in

addition to pavement texture. Innovative friction measuring devices are constantly being

developed with the measuring mechanisms of each being different from the others.

However, most of the current devices in use have been found to produce significantly

different results when used on the same pavement [2]. This observation has led to

 

2

 

research regarding harmonization of devices and standardization of the friction

evaluations.

1.2 Principles of Pavement Friction

The coefficient of pavement friction, µ, is defined as follows:

μ= FW

(1a)

where F is the friction force exerted by the pavement on a wheel and W is the normal

load of the device acting on that pavement. However, full-scale friction testing devices

quantify and report pavement friction as the Skid Number, SN, defined as;

SN=100*μ (1b)

It has been shown that the slip speed, S, at which friction is measured, has a significant

effect on the value of the measured SN.

S= *%Slip (1c)

where VV is the vehicle speed and the Percent Slip is determined by Equation 1d.

%Slip (1d)

VT is the speed of rotation of the tire during the test. The Penn State Model [1] expresses

the speed dependency of SN as follows;

SNS=SN0e- PNG100 S (2)

where SNS is the skid number measured at a slip speed of S, SN0 is the skid number at

zero speed, and PNG is the percent normalized gradient expressing the rate of decrease of

friction with speed. SN0 is a factor that has been highly correlated to the pavement

microtexture, and PNG is presumed to be dependent only on the pavement macrotexture.

 

3

 

SN0 and PNG can be determined from linear regression of friction data at various speeds

using Equation 2.

In order to address the need for standardization of measurement of different

devices, the Permanent International Association of Road Congresses (PIARC) [2] met in

France in 1995 to coordinate and conduct an experiment to standardize full-scale

pavement friction testing. This experiment, known as the International PIARC

Experiment to Compare and Harmonize Texture and Skid Resistance Measurements,

encompassed sixty-seven parameters from fifty-four pavement sites measured by forty-

seven different devices from sixteen countries [2]. Based on the analysis of the results,

the International Friction Index (IFI) concept was developed. Subsequently, the American

Society for Testing and Materials (ASTM) adopted the IFI and formulated the Standard

Practice for Calculating International Friction Index of a Pavement Surface (E1960-07-

2009) [3].

The IFI standard is a calibration method in which full-scale friction testers are

calibrated against a static friction tester, the Dynamic Friction Tester (DFT). The DFT

measured friction value at 20 km/h, DFT20, is used as a baseline for calibration. In order

to express the speed dependency of friction, the following PIARC model has been

developed by revising the Penn State Model [2];

FRS=FR0e- SSP (3)

where FRS is friction measure at a slip speed S, FR0 is the friction at zero speed, and SP is

the speed gradient which expresses the rate at which friction reduces with speed. Just as

in the case of the original Penn State Model [2] in Equation 2, FR0 has been highly

correlated to pavement microtexture, while SP has been shown to be correlated to a

 

4

 

pavement’s mean profile depth (MPD). The CT Meter is the standard laser device that is

recommended for evaluation of the macrotexture of a pavement in terms of MPD. FR0

and SP can be found using linear regression of friction data acquired at varying speeds,

using Equation 3.

In order to calibrate full-scale friction measuring devices using Equation 3, the

FR60 values of a given pavement measured with a full-scale device are compared to the

F60 values gathered by the DFT on the same pavement [2]. The FR60 values are found by

converting friction values found at various speeds back to the friction value at 60 km/h

using the SP value of the pavement measured with the CT meter using the rearranged

form of Equation 4;

FR60=FRSe- S-60SP (4)

Then, using linear regression of the corresponding values of FR60 and F60 for several test

sections, the following calibration equation can be developed and subsequently applied to

standardize pavement friction measurements at any speed;

F60=A+B*FR60 (5)

where A and B device specific constants. Finally, using F60 from Equation 5 and the SP

readings obtained from the CT Meter, the International Friction Index (IFI) of a pavement

is reported as [F60, SP] [2].

1.3 Locked-Wheel Skid Tester

Among the many different types of full-scale friction measuring devices, the

Locked-Wheel Skid Tester (LWT) has been known to collect the repeatable and

consistent data. It is for this reason that State Departments of Transportation (DOT) and

 

5

 

the Federal Highway Administration (FHWA) have adopted the LWT as the standard

friction measuring device. The LWT is a full slip device, since the measurements are

carried out at a slip of 100 percent with the measuring wheel completely locked during

testing. ASTM regulates the manufacturing and measuring standard of the LWT in

Standard Test Method for Skid Resistance of Paved Surfaces Using a Full-Scale Tire

(E274-06-2009) [4].

1.4 Limitations of the International Friction Index

The above IFI concept has inherent limitations because the dynamic effects

experienced by full-scale testing devices such as the LWT are not fully expressed when

calibrated against a static testing device such as the DFT. It has been documented that

pavement long-wave roughness has a significant effect on the measured skid values [5].

Pavement long-wave roughness, also known as the megatexture, causes the normal load

of the measuring device to fluctuate. This normal load fluctuation can be quantified by

the Dynamic Load Coefficient, DLC, expressed as;

DLC= σWWSTATIC

(6a)

where σW is the standard deviation of the normal load and WSTATIC is the static weight of

the device. An increased DLC over a pavement section has been shown to lower the skid

values measured by the LWT [5]. This effect is seen to affect the calibrated IFI values of

pavements that produce significantly high DLC values.

The factor contributing to the variation of the measured skid resistance with the

DLC is the dependency of the measured skid values on the normal load. Fuentes et al. [5]

 

6

 

showed that the following approximate equation can be used to express the relationship

between normal load and SN;

SN=SNi+SNi-SNr

1+e-(W-wi)

b

(6b)

where SNi is the SN at relatively low normal loads, SNr is the SN at relatively high

normal loads, W is the instantaneous normal load, and wi and b are parameters specific to

the LWT. Fuentes’ pavement friction dependency on normal load deviations can be

compared to the empirical equation developed by Schallamach [6] to express the

dependence of rubber friction on the normal load;

μ=cW - 13 (7)

where µ is the observed friction, W is the normal load, and c is dependent on the velocity.

1.5 Objectives of Study

Due to the above discussed limitations of the IFI and the observed effect of DLC

on measured skid values, an investigation was proposed to further quantify the effects of

DLC on the IFI. By theoretically modeling the dynamics of the LWT and comparing the

model’s predicted behavior with the corresponding field measurements, the effect of

pavement roughness on the IFI calibration standard would be quantified.

 

7

 

CHAPTER 2

EXPERIMENTAL ANALYSIS AND RESULTS

2.1 Proposed Vibration Modeling System

In previous research completed at the University of South Florida (USF) [5], it

was shown that the dominant natural frequency of the LWT is approximately 1.9 Hz. An

additional natural frequency around 11 Hz was also revealed, but with a nearly damped

out corresponding deflection. Therefore, a damped two-degree of freedom system with a

dominant natural frequency close to 1.9 Hz is proposed to model the LWT appropriately.

Figure 2.1 illustrates the proposed model and the associated parameters;

Figure 2-1: Two Degree of Freedom System with Displacement Input

M1 is the mass of the first degree of freedom of the model, and its displacement is given

by the function q1(t). K1 and C1 are the respective spring constant and damping value for

the first degree of freedom of the model. M2 is the mass of the second degree of freedom

 

8

 

of the model, and its displacement is given by the function q2(t). K2 and C2 are the

respective spring constant and damping value for the second degree of freedom of the

model. The input for the proposed model is a displacement corresponding to the

pavement profile, y=f(x), that is transformed into a time dependent vertical displacement

input, y=f(t), using the following equation;

t= xS (8)

where x is the longitudinal distance along the pavement profile, and S is the speed of the

LWT. The proposed modeling program was built around the following equation of

motion in space state form;

z=Az+By+Cy (9)

where z is the array of state of variables in Equation 10, A, B, and C, are array variables

in Equations 11, 12, and 13, y is the first derivative of the pavement profile with respect

to time, and is the first derivative of the variable z.

z=[q2 q2 q1 q1] (10)

A=

0 1 0 0 - K2

M2

0K2M1

- C2

M2

K2M2

C2M2

0 0 1C2M1

- (K2+K1)M1

- (C2+C1)M1

(11)

B= 0 0 0 K1M1

T (12)

C= 0 0 0 C1M1

T (13)

Using the above variables, the following numerical forms of the first and second

derivatives of the displacement functions, q1(t) and q2(t), were used to solve for the

system’s response explicitly;

 

9

 

qi t = qi t+∆t -qi t-∆t2∆t

(14)

qi t = qi t+∆t +qi t-∆t -2qi(t)

∆t2 (15)

A Microsoft Excel program, LWT Prediction Model, was developed to solve Equations 8-

15 and hence model the response of two degree of freedom systems.

2.2 Verification of the Program

Due to the fact that the developed program has the capacity to model any given

two degree of freedom system that experiences a time dependent displacement input,

several verifications were conducted to ensure the accuracy of the program. These

verifications are outlined in the following sections.

2.2.1 Modeling of a Two Degree of Freedom System Without Damping

Since the vibration response of damped systems is relatively complex, the

verifications started with an undamped two degree of freedom system. Das [7] shows that

the natural frequencies of an undamped two degree of freedom system can be found using

the following closed form solutions:

ω1n= 1√2

K1+K2M1

+ K2M2

+ K1+K2M1

- K2M2

2+ 4K2

2

M1M2

12

12

(16)

ω2n= 1√2

K1+K2M1

+ K2M2

- K1+K2M1

- K2M2

2+ 4K2

2

M1M2

12

12

(17)

 

10

 

where the parameters are described by the proposed model in Figure 2-1. Table 2-1

shows the parameters for one sample model in which undamped natural frequencies were

obtained using the above closed form solutions.

Table 2-1: Model Parameters for a Two Degree of Freedom System Without Damping

M2 100 Kg M1 100 Kg C2 0 N*s/m C1 0 N*s/m K2 10000 N/m K1 10000 N/m

The frequency spectrum was generated for the above system using the computer program

LWT Prediction Model. This is shown in Figure 2-2, which displays the system’s two

natural frequencies at 16.2 Hz and 6.2 Hz. From the closed-form solutions in Equations

16 and 17, the natural frequencies were found to be 16.180 Hz and 6.180 Hz respectively.

Figure 2-2 also shows that the frequency response of the program agrees well with the

corresponding closed-form solutions.

2.2.2 Modeling of an Uncoupled Two Degree of Freedom System With Damping

The natural frequencies of some damped two degree of freedom systems can be

found by uncoupling the damping parameters from the stiffness parameters and solving

the eigenvalue problem. To verify that the response of the developed program was

accurate with damping, a solved example from Inman [8] was modeled for verification of

the program. Table 2-2 shows the system parameters of the damped vibration system

used in this case.

 

11

 

Figure 2-2: Frequency Spectrum of a Two Degree of Freedom System Without Damping

Table 2-2: Model Parameters for a Two Degree of Freedom System With Damping

M2 1 Kg M1 1 Kg C2 1 N*s/m C1 2 N*s/m K2 4 N/m K1 5 N/m

According to Inman’s solution, the natural frequencies of the first and second degrees of

freedom of the system described by Table 2-2 are 3.33 Hz and 1.343 Hz respectively. The

above system was then used as an input in the computer program LWT Prediction Model

and the frequency spectrum was generated to determine the two natural frequencies.

Figure 2-3 shows that the program results agree well with the two natural frequencies

derived by Inman [8].

0

5

10

15

20

25

30

0 5 10 15 20 25

Am

plitu

de, A

(m)

Frequency, ω (s-1)

q1(t)q2(t)

 

12

 

Figure 2-3: Frequency Spectrum of a Two Degree of Freedom System With Damping

2.2.3 Modeling of a One Degree of Freedom System With Damping

Damped one degree of freedom systems can be solved relatively easily for their

natural frequencies. Due to this fact, a two degree of freedom system was selected to

emulate the response of two one degree of freedom systems by each time restraining one

of the degrees of freedom. In the first of these two cases, the degree of freedom of M2

was restricted using the parameters presented in Table 2-3, and the natural frequency of

the first degree was determined using the following basic equations [8];

ωin= KiMi

(18a)

ζi=Ci

2 KiMi (18b)

ωid=ωin 1-ζi (18c)

00.010.020.030.040.050.060.070.08

0 5 10 15 20 25 30

Am

plitu

de, A

(m)

Frequency, ω (s-1)

q1(t)q2(t)

 

13

 

where Mi, Ki, and Ci correspond to the parameters of the model in Figure 2-1, ni is the

undamped natural frequency of the ith degree of freedom, i is the damping ratio of the ith

degree of freedom, and di is the damped natural frequency of the ith degree of freedom.

Table 2-3: Model Parameters for a One Degree of Freedom System Restricting the

Motion of M2

M2 10 Kg M1 1000 Kg C2 0 N*s/m C1 5000 N*s/m K2 20000 N/m K1 20000 N/m

According to Equations 18a-18c, the natural frequency of the first degree of the above

system is 3.708 Hz. Then, the above parameters were input to the program and a

frequency spectrum was generated to determine the system’s natural frequency. Figure 2-

4 shows that the corresponding natural frequency is 3.7 Hz. Also, one can see that the

first and second degrees of freedom coincided, thus verifying the simplified one degree of

freedom motion anticipated in this case.

In the second case, M1 was made to always follow the input displacement

function of the pavement profile. This would allow the second degree of freedom to act

freely and describe a single degree of freedom motion. This condition was achieved using

the parameters outlined in Table 2-4. The corresponding damped natural frequency of the

second degree of freedom was found to be 3.708 Hz using Equations 18a-18c. The above

system was then modeled using the program LWT Prediction Model, and a frequency

spectrum was generated to determine the damped natural frequency. Figure 2-5 shows the

 

14

 

frequency response producing a natural frequency of 3.7 Hz thus verifying the accuracy

of the computer program.

Figure 2-4: Frequency Spectrum of the One Degree of Freedom System Restricting the Motion of M2

Table 2-4: Model Parameters for a One Degree of Freedom System Restricting the Motion of M1

M2 1000 Kg M1 - Kg C2 5000 N*s/m C1 - N*s/m K2 20000 N/m K1 - N/m

00.0050.01

0.0150.02

0.0250.03

0.0350.04

0 2 4 6 8 10 12

Am

plitu

de, A

(m)

Frequency, ω (s-1)

q1(t)q2(t)

 

15

 

Figure 2-5: Frequency Spectrum of the One Degree of Freedom System Restricting the Motion of M1

2.3 Determination of LWT Parameters Using Modeling Techniques

After verifying the accuracy of the computer program LWT Prediction Model, it

was necessary to determine the parameters of a damped two degree of freedom system

that closely matched the vertical response of the LWT to any pavement profile. In order

to do this, trial combinations of model parameters were iteratively input to the program

and the corresponding frequency was determined until the experimentally dominant

natural frequency was obtained by the model [5]. As mentioned in Section 2.1, the

measured dominant natural frequency of the LWT from previous research [5] was shown

to be around 1.9 Hz. Table 2-5 demonstrates the parameters of a system that closely

matches the response of the LWT, in terms of the predominant natural frequency.

The frequency response of the modeled two degree of freedom system is

represented in Figure 2-6. It is seen that the modeled natural frequency is around 1.9 Hz,

which closely matches the experimentally measured dominant natural frequency of 1.9

00.0050.01

0.0150.02

0.0250.03

0.0350.04

0 2 4 6 8 10 12

Am

plitu

de, A

(m)

Frequency, ω (s-1)

q1(t)q2(t)

 

16

 

Hz. The second experimental natural frequency of the LWT was seen to be around 11 Hz,

but its amplitude was almost completely damped out. Therefore, the second natural

frequency of the above modeled system is insignificant.

Table 2-5: Parameters of a Two Degree of Freedom System Representing the LWT

M2 440 Kg M1 60 Kg C2 1000 N*s/m C1 250 N*s/m K2 5000 N/m K2 2000 N/m

Figure 2-6: Frequency Spectrum of a Two Degree of Freedom System Representing the LWT

2.4 Verification of LWT Parameters Using Field Measurements

In order to model the friction response of the LWT correctly, a comparison was

made between the experimental response of the LWT for a given profile to that of the

program LWT Prediction Model for the same profile. The Profile H tested for this

0.000.010.020.030.040.050.060.070.080.090.10

0 5 10 15 20

Am

plitu

de, A

(m)

Frequency, ω (s-1)

q1(t)q2(t)

 

17

 

purpose is shown in Figure 2-7. A series of field tests was conducted at different speeds

over the above profile to determine the real time (actual) response of the LWT. This

spatial profile was first converted to a time dependent profile for modeling purposes.

Finally the profile was input to the computer-based LWT model and normal load

response of the modeled LWT was predicted. Figures 2-8, 2-9, and 2-10 show the actual

normal load response of the LWT at 20, 40, and 60 mph plotted against the response of

the modeled system.

Figure 2-7: Longitudinal Profile of Pavement H

Review of Figures 2-8, 2-9, and 2-10 reveals that the modeled response is more accurate

at higher speeds than at lower speeds. This could be attributed to the back torque created

by the frictional force which at lower speeds causes the trailer to bounce more

vigorously. However, the back torque effects cannot be modeled using the author’s

simplified system.

-0.25-0.20-0.15-0.10-0.050.000.050.100.150.200.25

0 10 20 30 40 50 60 70 80

Vert

ical

Dis

plac

emen

t, y

(m)

Longitudinal Distance, x (m)

 

18

 

Figure 2-8: Comparison of Experimental and Modeled Response of LWT at 20 mph

Figure 2-9: Comparison of Experimental and Modeled Response of LWT at 40 mph

600

700

800

900

1000

1100

1200

0 20 40 60 80

Nor

mal

Loa

d, W

(lbs

.)

Distance, x (m)

LWT @ 20 mphLWT @ 20 mphLWT @ 20 mphModel @ 20 mph

600700800900

10001100120013001400

0 20 40 60 80

Nor

mal

Loa

d, W

(lbs

.)

Distance, x (m)

LWT @ 40 mphLWT @ 40 mphLWT @ 40 mphModel @ 40 mph

 

19

 

Figure 2-10: Comparison of Experimental and Modeled Response of LWT at 60 mph

Although the overall response of the LWT at 20 mph is not predicted accurately, the

predicted average is close to those of the actual response thus showing that the model is

somewhat valid even at lower speeds such as 20 mph. On the other hand, at speeds of 40

mph and 60 mph, the deviations in normal load are much more accurate, and prove that

the proposed two degree of freedom system represents the response of the LWT more

accurately over a given profile at higher speeds.

2.5 Determination of the Relationship Between the Friction and Normal Loads

One objective of this research is to accurately predict the pavement friction

measured by an LWT using a two degree of freedom system. After verifying that the

normal load deviations are accurately modeled, the next step was to verify the friction

predictions of the LWT. In order to predict the frictional force experienced by the LWT

on any given pavement, the relationship of friction load to normal load on that pavement

0200400600800

10001200140016001800

0 20 40 60 80 100

Nor

mal

Loa

d, W

(lbs

.)

Distance, x (m)

LWT @ 60 mphLWT @ 60 mphLWT @ 60 mphModel @ 60 mph

 

20

 

must be determined. In order to perform this task, the relationship between the skid

number, SN, and the normal load proposed by Fuentes et al. [5] in equation (6b) will be

used. The experimental procedure followed by Fuentes et al. [5] to determine this

relationship for a given pavement is rigorous and painstaking. Thus, in order to avoid

recreating this experiment, the friction data obtained by Fuentes et al. [5] in the above

experiment was used in the author’s analysis. Table 2-6 contains the friction data

presented by Fuentes et al. [5] for two Pavements C and D. Figures 2-11 and 2-12

illustrate the relationship determined from Equation 6b for speeds of 30 and 55 mph

respectively.

The frictional force vs. normal load relationship is deduced by simply multiplying

the SN by the corresponding normal load at any selected point on the curves in Figures 2-

11 and 2-12. Figures 2-13 and 2-14 illustrate the corresponding relationships between

frictional force and normal load derived from Figures 2-11 and 2-12 respectively.

Table 2-6: Parameters for the SN vs. W Relationship for Pavements C and D (Fuentes et al., 2010)

Pavement Speed SNi ln(SNi) SNr ln(SNr)

C 30 47.5 3.861 41.5 3.726 C 55 42.5 3.750 36.4 3.595 D 30 51.7 3.945 34.5 3.541 D 55 35 3.555 21 3.045

 

21

 

Figure 2-11: SN vs. W Relationship at 30 mph (Fuentes et al., 2010)

Figure 2-12: SN vs. W Relationship at 55 mph (Fuentes et al., 2010)

0

10

20

30

40

50

60

0 500 1000 1500 2000 2500 3000

Skid

Num

ber,

SN

Normal Load, W (lbs.)

Pavement CPavement D

05

1015202530354045

0 500 1000 1500 2000 2500 3000

Skid

Num

ber,

SN

Normal Load, W (lbs.)

Pavement CPavement D

 

22

 

Figure 2-13: Derived Relationship of Frictional Force to Normal Load at 30 mph

Figure 2-14: Derived Relationship of Frictional Force to Normal Load at 55 mph

In order to model the SN vs. normal load at speeds other than 30 and 55 mph, a

logarithmic re-arrangement of the fundamental friction-speed relationship in Equation 3

can be used as shown in Equation 19.

ln(SN)=- SSP

+ln(SN0) (19)

0

200

400

600

800

1000

1200

0 500 1000 1500 2000 2500 3000

Fric

tion

Loa

d, F

(lbs

.)

Normal Load, W (lbs.)

Pavement CPavement D

0100200300400500600700800900

1000

0 500 1000 1500 2000 2500 3000

Fric

tion

Loa

d, F

(lbs

.)

Normal Load, W (lbs.)

Pavement CPavement D

 

23

 

Figures 2-15 and 2-16 depict how the relationships of SNi and SNr versus speed were

determined respectively using Equation 19 for Pavement C and D for a range of speeds

used in the current analysis.

Figure 2-15: Relationship between SNi and Speed

Figure 2-16: Relationship between SNr and Speed

Pavement Cy = -0.0044x + 3.9942

Pavement Dy = -0.0156x + 4.4136

3.003.103.203.303.403.503.603.703.803.904.00

0 20 40 60

ln (S

Ni)

Speed, S (mph)

Pavement C

Pavement D

Pavement Cy = -0.0052x + 3.883

Pavement Dy = -0.0199x + 4.1367

3.003.103.203.303.403.503.603.703.80

0 20 40 60

ln (S

Nr )

Speed, S (mph)

Pavement C

Pavement D

 

24

 

Tables 2-7 and 2-8 contain data on the variations of SNi and SNr with speed generated

using Figures 2-15 and 2-16 for Pavements C and D.

Table 2-7: Parameters for Projection of SN vs. Normal Load Relationship Across a

Range of Speeds for Pavement C (Fuentes et al., 2010)

Pavement Speed SNi ln(SNi) SNr ln(SNr) C 20 49.710 3.906 43.772 3.779 C 25 48.628 3.884 42.649 3.753 C 30 47.570 3.862 41.554 3.727 C 35 46.535 3.840 40.488 3.701 C 40 45.522 3.818 39.449 3.675 C 45 44.532 3.796 38.436 3.649 C 50 43.563 3.774 37.450 3.623 C 55 42.615 3.752 36.489 3.597 C 60 41.687 3.730 35.552 3.571

Table 2-8: Parameters for Projection of SN vs. Normal Load Relationship Across a Range of Speeds for Pavement D (Fuentes et al., 2010)

Pavement Speed SNi ln(SNi) SNr ln(SNr)

D 20 60.437 4.102 42.043 3.739 D 25 55.902 4.024 38.061 3.639 D 30 51.707 3.946 34.457 3.540 D 35 47.827 3.868 31.193 3.440 D 40 44.239 3.790 28.239 3.341 D 45 40.919 3.712 25.564 3.241 D 50 37.849 3.634 23.143 3.142 D 55 35.009 3.556 20.951 3.042 D 60 32.382 3.478 18.967 2.943

Then, the data shown in Tables 2-7 and 2-8 can be used to model the SN vs. normal load

relationship for Pavements C and D at any speed using Equations 6b and 19.

 

25

 

2.6 Verification of Friction Load Modeling

After determining the relationship of friction load to normal load, an experimental

verification was extended to ensure that the program models correctly the friction load

experienced by the LWT as well. Using Equation 6b and the data from Tables 2-7 and 2-

8 combined with the normal load deviation prediction capability of the modeling program

LWT Prediction Model, an attempt was made to predict the pavement friction on

Pavement H.

Since the experimental procedure to determine the relationships of skid number

and friction to normal load were not recreated for Pavement H, it was assumed that the

curve corresponding to Pavement H was geometrically similarly to that of Pavement D in

Fuentes’ experimentation. Therefore, SN versus normal load (Figure 2-12) and friction

load versus normal load (Figure 2-14) curves were replotted in Figures 2-17 and 2-18. In

the experiment conducted by Fuentes et al. [5], the SN0 in Equation 6b was found to be

the same as the SN value of the pavement under normal loads used in standard LWT

testing conditions. Thus, assuming that the SN measured at the standard LWT normal

load for Pavement H as SN0 corresponding to that pavement, curves for Pavement H in

Figures 2-17 and 2-18 were generated for SN and friction load.

Then, friction tests were conducted on Pavement H using the LWT, and those

results were compared to the responses predicted by the modeling program. Figure 2-19

shows the comparison of the model predictions to the actual test results conducted in

three trials.

 

26

 

Figure 2-17: Relationship of SN vs. Normal Load for Pavement H at 55 mph

Figure 2-18: Relationship of Friction Load vs. Normal Load for Pavement H at 55 mph

05

1015202530354045

0 500 1000 1500 2000 2500 3000

Skid

Num

ber,

SN

Normal Load, W (lbs.)

Pavement CPavement DPavement H

0100200300400500600700800900

1000

0 500 1000 1500 2000 2500 3000

Fric

tion

Loa

d, F

(lbs

.)

Normal Load, W (lbs.)

Pavement CPavement DPavement H

 

27

 

Figure 2-19: Comparison of Model Prediction to the Results of Friction Tests

As one can see from Figure 2-19, the friction load of the pavement is reasonably

accurately modeled by the program LWT Prediction Model. The average SN of the skid

tests was 29.6, while the program predicted an average of 30.3.

2.7 Modeling the Effects of Pavement Roughness on the IFI

After verifying that the modeling program correctly modeled the normal load and

the frictional load deviation of the LWT, friction data from the Fuentes experiment [5]

were used to determine the effects of pavement roughness on the IFI parameters. In order

to achieve this, an analysis was performed to investigate the individual effects of

frequency and amplitude variations on the SN predicted by the program LWT Prediction

Model.

First, a range of pavement profiles with varying frequencies with identical

amplitudes were modeled by the program LWT Prediction Model to determine the effects

0

100

200

300

400

500

600

0 20 40 60 80 100

Nor

mal

Loa

d, W

(lbs

.)

Distance, x (m)

LWT @ 55 mphLWT @ 55 mphLWT @ 55 mphModel @ 55 mph

 

28

 

of the frequency variations on the friction-speed relationship. Table 2-9 shows the input

values of the modeling program.

Table 2-9: Inputs for Frequency Variation Analysis (A = 0.25 m)

Pavement Frequency, ω (Hz) C 0.00 0.05 0.50 5.00 D 0.00 0.05 0.50 5.00

Figures 2-20 and 2-21 display the results corresponding to the above input values.

Figure 2-20: Frequency Variation Effects on the Friction-Speed Relationship of Pavement C

The SN0 evaluated from these plots is the friction value at zero speed. The magnitudes of

SN0 and the changes of the slope of the friction-speed relationship (speed gradient) for

Pavements C and D are shown in Table 2-10. As seen in Table 2.10, for a given

pavement, as the frequency increases the gradient of the friction versus speed curve

3.603.653.703.753.803.853.903.95

0 20 40 60 80

ln (S

N)

Speed , S (mph)

ω = 0.00 Hzω = 0.05 Hzω = 0.50 Hzω = 5.00 Hz

 

29

 

increases while the SN0 remains more or less constant. Though the gradient increases, the

SP decreases as defined in Equation 19.

Figure 2-21: Frequency Variation Effects on the Friction-Speed Relationship of Pavement D

Table 2-10: Results of Frequency Variation Analysis on Pavements C and D

Pavement Characteristics Frequency, ω (Hz) Speed Gradient, SP SN0 Pavement C 0.00 227.27 54.21Pavement C 0.05 227.27 54.22Pavement C 0.50 217.39 54.39Pavement C 5.00 200.00 52.28Pavement D 0.00 64.10 82.29Pavement D 0.05 63.69 82.36Pavement D 0.50 61.35 83.20Pavement D 5.00 56.18 75.71

Similar to the previously performed frequency variation analysis, an amplitude

variation analysis was conducted on Pavements C and D. Table 2-11 demonstrates the

input values used in the program LWT Prediction Model. Figures 2-22 and 2-23 display

the results of the inputs from Table 2-11.

3.00

3.20

3.40

3.60

3.80

4.00

4.20

0 20 40 60 80

ln (S

N)

Speed , S (mph)

ω = 0.00 Hzω = 0.05 Hzω = 0.50 Hzω = 5.00 Hz

 

30

 

Table 2-11: Inputs for Frequency Variation Analysis (ω = 0.05 Hz)

Pavement Amplitude, A (m) C 0.00 0.05 0.50 5.00 D 0.00 0.05 0.50 5.00

The magnitudes of SN0 and the changes of the slope of the friction-speed relationship

(speed gradient) for Pavements C and D are shown in Table 2-12. As seen in Table 2.12,

for a given pavement, as the amplitude increases, the gradient of the friction versus speed

curve increases while SN0 remains more or less constant. Though the gradient increases,

the SP decreases as defined in Equation 19.

Figure 2-22: Amplitude Variation Effects on the Friction-Speed Relationship of Pavement C

3.603.653.703.753.803.853.903.95

0 20 40 60 80

ln (S

N)

Speed , S (mph)

A = 0.00 mA = 0.05 mA = 0.50 mA = 5.00 m

 

31

 

Figure 2-23: Amplitude Variation Effects on the Friction-Speed Relationship of Pavement D

Table 2-12: Results of Amplitude Variation Analysis on Pavements C and D

Pavement Characteristics Amplitude, A (m) Speed Gradient, SP SN0 Pavement C 0.00 227.27 54.21Pavement C 0.05 227.27 54.21Pavement C 0.50 222.22 54.29Pavement C 5.00 200.00 53.91Pavement D 0.00 64.10 82.29Pavement D 0.05 64.10 82.29Pavement D 0.50 63.29 82.67Pavement D 5.00 56.18 82.22

Due to the limited amount of data on the SN versus normal load relationship for different

types of pavements, this analysis was designed to illustrate typical results that would be

seen on most pavements.

3.00

3.20

3.40

3.60

3.80

4.00

4.20

0 20 40 60 80

ln (S

N)

Speed , S (mph)

A = 0.00 mA = 0.05 mA = 0.50 mA = 5.00 m

 

32

 

2.8 Field Verification of the Effects of Pavement Roughness on the IFI

As shown in Section 2.7, pavement roughness can have a significant effect on the

measured SN values and hence the computation of the IFI. Another aspect of the Fuentes

[5] experimentation consisted of analyzing the effects of pavement roughness on

measured skid values. Based on the analysis in Section 2.7, the variation in SP can be

significantly different depending on the frequency and amplitude variations along a given

pavement. This difference was verified in the field using data from Fuentes’ [5] original

experiment, as well as friction tests conducted on an alternative Pavement I located in

Brandon, Florida. The friction testing on Pavement I was conducted using the same

protocol used by Fuentes to ensure that the results would not be skewed. In this regard,

two sections were evaluated on Pavement I with one section found to be relatively

rougher compared to the other, based on the significantly different profiles.

After evaluating the macrotexture using the CT Meter to ensure that macrotexture

was identical on both of those sections, skid tests were performed on the two pavement

sections with significantly different profiles. Reformulation of data from Fuentes’ [5]

experiment on Pavement B is shown in Figure 2-24, with Table 2-13 displaying the

values of SN0 and SP. The values of SN0 from these two sections are not significantly

different, and it can be inferred from regression that the friction at zero speed is invariant

for both pavement sections. On the other hand, Figure 2-25 shows the data from testing

of Pavement I with Table 2-14 displaying the values of SN0 and SP.

 

33

 

Figure 2-24: Effect of Pavement Roughness on IFI Parameters for Pavement B

Table 2-13: Results from Pavement Roughness Analysis on Pavement B

Section Speed Gradient, SP SN0 Smooth 100.00 49.74 Rough 74.63 44.46

Figure 2-25: Effect of Pavement Roughness on IFI Parameters for Pavement I

2.502.702.903.103.303.503.703.90

0 10 20 30 40 50 60

ln(S

N)

Speed, S (mph)

RoughSmooth

3.653.703.753.803.853.903.954.004.054.104.15

0 10 20 30 40 50

ln(S

N)

Speed, S (mph)

RoughSmooth

 

34

 

Table 2-14: Results from Pavement Roughness Analysis on Pavement I

Section Speed Gradient, SP SN0 Smooth 92.59 73.05 Rough 93.46 61.52

The values of SN0 for both sections on Pavement B is more or less constant, while the SP

decreases as the roughness increases. This follows the predictions made by the program

LWT Prediction Model. However, the values of SN0 for both sections of Pavement I are

significantly different, and it was concluded that regression data is needed from higher

speeds to make an appropriate conclusion about their relationship. The SP variation for

the Pavement I sections also does not conform to previous findings in this work, and it

was concluded that tests at higher speeds are needed to determine to true gradients of

each section of pavement. Review of these two sets of data shows that the IFI parameters

must be calculated from a larger range of speeds in order to be valid.

2.9 Modeling the Effects of the Normal Load versus Friction Load Relationship

The friction load predictions for the LWT were made in this work primarily based

on the relationship between SN and normal load developed by Fuentes [5]. Therefore it is

clear that the relationship of SN to normal load is critical to predicting the friction load

response of the LWT from the program LWT Prediction Model. Hence, an investigation

was conducted to explore in detail the effects of the above relationship on skid resistance

measurements.

Equation 20 expresses ΔSN, which is maximum difference between SN observed

during changes in the normal load of a given pavement and hence expressed by;

∆SN=SNi-SNr (20)

 

35

 

Using data from Pavement C in the Fuentes [5] experiments, three other hypothetical

pavements (Pavement E, F, and G) were created with the same SNi but having different

ΔSN values to model the effects of the friction-speed relationship measured with the

LWT. Figure 2-26 displays the representative SN versus normal load relationships of the

pavements used in the above analysis, while Figure 2-27 shows the variation of ΔSN

versus speed of the hypothetical pavements matching that of Pavement C.

Figure 2-26: Relationship of SN vs. Normal Load for Pavements C, E, F, and G at 55 mph

Using the data in Figures 2-26 and 2-27 an analysis was performed with the program

LWT Prediction Model to determine the effect of ΔSN of a given pavement on measured

friction values. While the results are displayed in Figure 2-28, and the magnitudes of the

changes are displayed in Table 2-15.

05

1015202530354045

0 500 1000 1500 2000 2500 3000

Skid

Num

ber,

SN

Normal Load, W (lbs.)

Pavement CPavement EPavement FPavement G

 

36

 

Figure 2-27: Variation in ΔSN versus Speed for Pavements C, E, F, and G

Figure 2-28: Effects of Variation in ΔSN for Pavements C, E, F, and G with Speed

0

5

10

15

20

25

30

0 20 40 60 80

Cha

nge

in S

kid

Num

ber,

ΔSN

Speed, S (mph)

Pavement CPavement EPavement FPavement G

3.65

3.70

3.75

3.80

3.85

3.90

3.95

0 20 40 60 80

ln (S

N)

Speed, S (mph)

Pavement CPavement EPavement FPavement G

 

37

 

Table 2-15: Results from ΔSN Variation Analysis on Pavements C, E, F, and G

Pavement Speed Gradient, SP SN0 Pavement C 217.39 54.39 Pavement E 200.00 54.54 Pavement F 185.19 54.71 Pavement G 227.27 54.28

The results in Table 2-15 confirm that the ΔSN of a given pavement can have a

significant effect on the speed gradient, SP, and hence the measured friction values. This

effect is also illustrated in Figures 2-24 and 2-25 where the pavements are seen to have

significant differences in particular the SP values. In summary, it can be concluded that

three factors will affect the computed IFI values of a rough pavement:

1. Frequency of roughness wave

2. Amplitude of roughness wave

3. SN dependence on the normal load (ΔSN)

2.10 Alternative Method for Determining Relationship Between SN and Normal

Load

In lieu of the rigorous method by which Fuentes [5] determined the relationship of

SN versus normal load for a given pavement, this study proposes a more practical method

for the convenience of implementation. Data from Pavement B in Fuentes’ [5]

experiment was reformulated to reflect the relationship given by Schallamach in Equation

7. The average normal loads of each section were normalized using a static LWT weight

of 1085 lbs. and then plotted against the corresponding SN of those tests. The basic form

of Equation 7 used in this analysis is given in the following equation;

 

38

 

SN=c WAVEWSTATIC

- a (21)

where c is the speed-dependent parameter, a is a parameter specific to the pavement type,

WAVE is the average normal load recorded during a more or less uniformly rough section,

and WSTATIC is the static weight of the LWT. Figure 2-29 shows the plots of Equation 21

at speeds of 25, 40 and 55 mph.

Figure 2-29: Relationship of SN vs. Normal Load for Pavement A at 25, 40, and 55 mph Using Schallamach’s Equation

Based on Figure 2-29, the mathematical form prescribed in Equation 21 seems to provide

a valid method for determining the relationship of SN versus normal load. The parameter

a is nearly identical at 40 and 55 mph, showing that a can be assumed to be invariant for

this pavement. The value of a at 25 mph is slightly different from those at 40 and 55 mph,

but friction testing at low speeds has been found to be relatively unreliable and

inconsistent due to the back-torque effect as outlined in Section 2.4. The values of c

25 mphy = 22.557x-6.931

R² = 0.9588

40 mphy = 16.199x-9.396

R² = 0.960155 mph

y = 14.854x-9.222

R² = 0.945505

101520253035404550

0.9 0.92 0.94 0.96 0.98 1

Skid

Num

ber,

SN

WAVE/WSTATIC

25 mph40 mph55 mph

 

39

 

decrease as speed increases, which follows the basic tenants of the friction-speed

relationship.

In order to develop these trends for other pavements, friction tests must be

conducted at least on two relatively rough and smooth sections of a given pavement, and

the resulting average normalized weights must be plotted against the average SN values

as in the case of Figure 2-29. This procedure was followed on Pavement I from Section

2.8, and the results are given in Figure 2-30.

Figure 2-30: Relationship of SN vs. Normal Load for Pavement I at 20, 30, and 40 mph

Using Schallamach’s Equation

Review of Figure 2-30 shows that the pavement parameter a varies slightly across the

speeds tested. Also, the speed-dependent parameter c is skewed at 40 mph. In addition,

the relatively low R2 at 40 mph indicates possible error in the data at that speed.

20 mphy = 12.893x-17.82

R² = 0.952430 mph

y = 9.9644x-18.69

R² = 0.902740 mph

y = 16.103x-11.04

R² = 0.8335

0

10

20

30

40

50

60

70

0.9 0.905 0.91 0.915 0.92 0.925 0.93

Skid

Num

ber,

SN

WAVE/WSTATIC

20 mph30 mph40 mph

 

40

 

CHAPTER 3

CONCLUSIONS AND RECOMMENDATIONS

3.1 Current Research Proponents

Evaluation and maintenance of pavement friction in a highway network is a

crucial aspect of transportation safety programs. Researchers have made significant

efforts to evaluate and standardize pavement friction measured with numerous full-scale

friction testers. In this work, an attempt has been made to understand the frictional

response of the LWT for a given profile. A two degree of freedom vibration model was

developed to simulate the LWT behavior and determine what effects pavement roughness

has on the LWT measured friction and hence the IFI value of a given pavement profile.

3.2 Contribution 1 - Theoretical Prediction of LWT Friction Values

As outlined in Section 2.6, measured friction values can be predicted accurately

using the program LWT Prediction Model developed in this study. The ability of the

program LWT Prediction Model to predict friction on a given pavement is governed by

the frictional dependency of that pavement on the normal load. This relationship was also

shown to affect significantly the reported values of the IFI due to its effect on the speed

gradient, SP. Further modification of this method must be pursued by better evaluating

the dependency of friction on the normal load.

 

41

 

3.3 Contribution 2 - Effects of Pavement Roughness on the IFI

As outlined in Section 2.7, pavement roughness can have significant effects on the

computed IFI values of a pavement. As the roughness of a pavement increases, the

friction-speed relationship is altered, thus changing the values of SP and F60. Using linear

regression of the data, it was shown that various friction-speed plots merge on a single

value of SN0 (SN at zero speed). The author’s LWT model predicts that generally the SP

of a pavement decreases as pavement roughness increases.

3.4 Contribution 3 - Effects of Frictional Dependency on Normal Load on the IFI

In lieu of the relatively complicated process in which the SN vs. W relationship

was developed by Fuentes [5], a new method was proposed to facilitate the prediction of

SN values from the developed program. Using the form prescribed by Schallamach and

the method outlined in Section 2.10, practitioners can accurately develop an appropriate

relationship between SN and normal load for a given pavement. Ideally, the parameters in

Equation 21 can be standardized based on macrotexture values, and then input into the

author’s model to accurately predict pavement friction over any given profile. Pavements

with large ΔSN values (maximum SN difference with respect to the normal load) were

shown to be more sensitive to roughness and produce larger deviations in the IFI

parameter. This effect can be minimized if pavements could be designed with materials

that exhibit a minimal SN variation (ΔSN). For instance, a pavement with ΔSN of zero

would exhibit no effects due to pavement roughness or elevated DLC.

 

42

 

LIST OF REFERENCES

[1] Leu, M.C. and J.J. Henry. “Prediction of Skid Resistance as a function of Speed from Pavement Texture,” Transportation Research Record 946, Transportation Research Board, National Council, Washington, D.C., 1983. [2] Wambold, J. C., C. E. Antle, J. J. Henry, and Z. Rado. “International PIARC Experiment to Compare and Harmonize Texture and Skid Resistance Measurements”. Final Report submitted to the Permanent International Association of Road Congresses (PIARC), State College, PA, 1995. [3] ASTM: “Standard Practice for Calculating International Friction Index of a Pavement Surface”, Standard No E1960-07, ASTM 2009 [4] ASTM: “Standard Test Method for Skid Resistance of Paved Surfaces Using a Full-Scale Tire”, Standard No E274-06, ASTM 2009 [5] Fuentes, L., M. Gunaratne, and D. Hess. “Evaluation of the Effect of Pavement Roughness on Skid-Resistance,” ASCE Journal of Transportation Engineering, Vol. 136 No. 7, Reston, Virginia, 2010. [6] Schallamach, A. “The Load Dependence of Rubber Friction”, Proc. Phys. Soc., Section B, Volume 65, Issue 9, pp. 657-661 (1952). [7] Das, B.M. “Fundamentals of Soil Dynamics”. New York: Elsevier Science Publishing Co., Inc., 1983. Print. [8] Inman, D. J., “Vibration with Control”. New York: John Wiley and Sons, Ltd, 2006. Print.